Find the equation of the line which passes through the point $(-4, 3)$ with slope $\frac{1}{2}$.

Find the equation of the line such that the perpendicular drawn from the origin to the line makes an angle of $30^{\circ}$ with the $x$-axis and the line forms a triangle of area $\frac{50}{\sqrt{3}}$ with the axes.

The minimum area of the triangle formed by the variable line $3 \cos \theta \cdot x + 4 \sin \theta \cdot y = 12$ and the coordinate axes is

$A$ line passes through $P(-4, 1)$ and meets the coordinate axes at points $A$ and $B$. If $P$ divides the segment $AB$ internally in the ratio $1:2$,then the equation of the line is

If a straight line is at a distance of $10$ units from the origin and the perpendicular drawn from the origin to it makes an angle of $\frac{\pi}{4}$ with the negative $X$-axis in the negative direction,then the equation of that line is:

What is the equation of the line passing through $(3, -4)$ and $(4, 3)$?